Absence Makes the Wins Grow Stronger

There are so many times in life when we all wish we would have abstained from a decision or response because it would have elicited a more desirable outcome. Whether in business, sports, politics, or everyday life, there are those situations where a null activity is better than one which requires some exertion. These situations are often most evident, however, on that stage that is perhaps the most widely observed – sports. While it’s often speculated that a coach would have been better served to take the conservative route or detracted from his pressure during a game, I’ve never seen it proven statistically that it’s advantageous. Given recent events, though, I decided to take some time here to determine whether doing nothing would have actually been better than doing something.

If you follow the NFL in any capacity, you’re probably familiar with the Week 6 Monday Night Football game where The Sheriff (Payton Manning) reared his majestic head and orchestrated a comeback victory on the road – the likes of which, we’ve never seen before. The game took place in San Diego, against the Chargers, where the Broncos achieved 35 unanswered points in the second half to overcome a 24-0 halftime deficit. Following the game, the majority of the storylines discussed Manning’s superior abilities as a quarterback, the Broncos stout defense, and Philip River’s inability to avoid interceptions. There was, however, no discussion about the efficacy of the coaching decisions. There were no commentators considering whether it would have been prudent to simply kill time – you know, the way a leading team typically does in the final two minutes of the game – for the entire second half. Would it be that absurd for the Chargers to effectively concede each down for the entire second half, simply to run the clock? Let’s find out.

How I Did It

In order to determine how effective running out the clock would have been for the Chargers, I used the following methods: First, I collected drive-by-drive data for the Broncos over the majority of this season. Second, I used this data to create cumulative probability distributions regarding the probability of scoring points on a drive (whether 7, 3, or 0 points). Third, I used this probability distribution to create a series of potential offensive drives for the Broncos over the course of the second half – where the result of each drive was randomly selected given the cumulative probability. I then determined how many offensive drives the Broncos would have had given the following three scenarios in order to determine the probability of scoring the requisite points (24). Finally, I employed 2,000 simulations for each scenario to calculate the precise probability of the Broncos scoring more than 24 points and beating the Chargers (2,000 simulations were used because the number is robust enough to eliminate the influence of any outliers).

For the calculations that correspond to the following scenarios, I used a few assumptions. First, I assumed the Broncos didn’t ever score “negative” points. “Negative” points would occur by allowing Chargers defensive touchdowns or turning the ball over in field goal range. I didn’t account for this because it would only really correspond to Scenario 3 and wouldn’t have really changed the result. Second, I didn’t account for Chargers taking any time outs because this all is presuming Chargers are wasting time, not conserving it. Third, I assumed all the Broncos time outs were used in the effort of saving clock consumption and not to frivolously adjust mistakes. This is consistent with the optimal nature of my scenarios below. Finally, I assumed Broncos made all the extra points taken because the probability of missing one is so insignificant, it wouldn’t have changed the results at all.

Scenarios and Results

Scenario 1 – Optimal and Almost Impossible Scenario

In Scenario 1, I calculated the simulations under the situation that Broncos defense stopped the Chargers for a 3-and-out each drive and the Broncos only took 3 full plays to either score or not. As such, each team would have only held the ball for 2 minutes (provided the NFL play clock is 40 seconds and time doesn’t run on the first down).

Probability of Broncos Winning in Scenario 1 = 35.58%

Scenario 2 – Outstanding Play and Slightly Less Impossible Scenario

Since Scenario 1 is somewhat contrived and nearly impossible to accomplish, I created Scenario 2 to represent outstanding play by the Broncos, but to be slightly more feasible. As a result, in Scenario 2, the Broncos are still able to ensure 3-and-outs for the Chargers offense, but take 3 minutes per drive to either score or not. This is more feasible because 3 minute drives, while still extraordinarily short, are much more frequent than 2 minute drives. Still, though, this assumes stopping the Chargers on each play and no turnovers.

Probability of Broncos Winning in Scenario 2 = 8.12%

Scenario 3 – Great Play and Somewhat Probable Scenario

In order to have at least one scenario that reflects would most frequently happens in the NFL, but still maintain the requisite great play by the Broncos to come back from such a deficit, Scenario 3 was created. In this scenario, the Chargers achieve 2 first downs in the half and the Broncos use 4 minute drives. Still, this requires great play from the Broncos, but is more representative of what typically happens around the league.

Probability of Broncos Winning in Scenario 3 = 3.75%

Final Thoughts

So there it is, folks! Had the Chargers simply engaged in a run-out-the-clock scheme for the entire second half, the probability of the Broncos winning, even under the most optimal of conditions, was only around 35%. In fact, in a more likely scenario, the Broncos would have only had a 3.75% chance of winning. Of course, looking at the game ex post, given what the Chargers actually did, the probability of the Broncos winning the game was 100%.

I would be very interested to hear the perspective of some “professional” sports analysts as to whether or not they agree with a potential scheme of draining the clock for the entire half. Given my own anecdotal experience, analysts dislike introducing change into the game they often played themselves. I’d wager most of the analysts would disagree with a proposed strategy that involves running no substantial plays. But the numbers don’t lie – in situations like this, sometimes it’s better to stay out of it!

In this case, absence really does make the wins grow stronger!